(a)
Find the error in the computation of maximum stress by assuming the bar as straight.
(a)
Answer to Problem 166P
The error in the computation of maximum stress by assuming the bar as straight is
Explanation of Solution
Given information:
The value of h is
The inner
The width and depth of the bar are
The moment (M) is
Calculation:
Calculate the cross-section area (A) of the bar as follows:
Substitute
Calculate the moment of inertia (I) of the cross-section of the bar using the relation:
Substitute
Calculate the distance (c) between the neutral axis and the extreme fiber using the relation:
Substitute
Calculate the stress
Substitute
Calculate the radius (R) of the neutral surface using the relation:
Substitute
Calculate the mean radius
Substitute
The distance (e) between the neutral axis and the centroid of the cross-section using the relation:
Substitute
Calculate the actual stress using the relation:
Substitute
Calculate the error in the computation of maximum stress by assuming the bar as straight using the relation:
Substitute
Thus, the in the computation of maximum stress by assuming the bar as straight is
(b)
Find the error in the computation of maximum stress by assuming the bar as straight.
(b)
Answer to Problem 166P
The error in the computation of maximum stress by assuming the bar as straight is
Explanation of Solution
Given information:
The value of h is
The inner
The width and depth of the bar are
The moment (M) is
Calculation:
Calculate the radius (R) of the neutral surface using the relation:
Substitute
Calculate the mean radius
Substitute
The distance (e) between the neutral axis and the centroid of the cross-section using the relation:
Substitute
Calculate the actual stress using the relation:
Substitute
Calculate the error in the computation of maximum stress by assuming the bar as straight using the relation:
Substitute
Thus, the in the computation of maximum stress by assuming the bar as straight is
(c)
Find the error in the computation of maximum stress by assuming the bar as straight.
(c)
Answer to Problem 166P
The error in the computation of maximum stress by assuming the bar as straight is
Explanation of Solution
Given information:
The value of h is
The inner radius
Show the unit conversion of inner radius as follows:
The inner
The width and depth of the bar are
The moment (M) is
Calculation:
Calculate the radius (R) of the neutral surface using the relation:
Substitute
Calculate the mean radius
Substitute
The distance (e) between the neutral axis and the centroid of the cross-section using the relation:
Substitute
Calculate the actual stress using the relation:
Substitute
Calculate the error in the computation of maximum stress by assuming the bar as straight using the relation:
Substitute
Thus, the in the computation of maximum stress by assuming the bar as straight is
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Chapter 4 Solutions
Mechanics of Materials, 7th Edition
- Pole AB is 12m. long and its weight W = 35kN. It is being lifted using BC and BD. When the pole is tilted at an angle of 60° from the x-axis, the resultant force acts at point A. 'p 2.6 m 3 m 4.5 m 3m 1. Find the tensile force (kN) in cable BC. В. 21.6 A. 22.5 C. 26.1 D. 28.2 2. Find the tensile force (kN) in cable BD. А. 13.1 В. 11.3 С. 14.5 D. 16.1 3. What is the value of the resultant (kN) acting at point A. В. 65.9 А. 69.5 C. 90.6 D. 56.9arrow_forwardPROBLEM 2.62 In a standard tensile test, a steel an aluminum rod of 20-mm diameter is subjected to a tension force of P = 30 kN. Knowing that v 0.35 and E= 70 GPa, determine (a) the elongation of the rod in a 150-mm gage length, (b) the change in diameter of the rod. - 20-mm diameter 150 mm 0.205 mm -0.00955 mmarrow_forwardChapter 4 : Stresses & Strains in Statically Indeterminate Structures I 53 EXERCISE 4.1 1. An alloy bar 800 mm long and 200 mm in cross-section is held between two rigid plates and is subjected to an axial load of 200 kN as shown in Fig. 4.7. | A В C 200 kN 300 500 Fig. 4.7 Find the reactions at the two ends A and C as well as extension of the portion AB. [Ans. 125 kN ; 75 kN ; 0.094 mm] 2. A bar ABC fixed at both ends A and Cis loaded by an axial load (P) at C. If the distances AB and BC are equal to a and b respectively then find the reactions at the ends A and C. 3. An axial force of 20 kN is applied to a steel bar ABC which is fixed at both ends A and C as shown in Fig. 4.8. 2 A = 200 mm A = 100 mm 20 kN+ A В 2 m 1 m Fig. 4.8 Determine the reactions at both the supports and stresses developed in two parts of the bar. Take E = 200 GPa. [Ans. R = R = 10 kN; oAR = 50 MPa (C); oBC = 100 MPa (7)] %3D %3! %3D 4. A prismatic bar ABCD has built-in ends A and D. It is subjected to two point…arrow_forward
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